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MGT 200 (28)
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Lecture 1

MGT 200 Lecture 1: Chapter 6 Class
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Department
Management
Course
MGT 200
Professor
Laufenberg
Semester
Spring

Description
Efficient Diversification Portfolio- collection of assets Firm specific risk- diversifiable/unsystematic/idiosyncratic/unique Market risk – nondiversifiable/systematic/macro Based off the market portfolio – all the assets in the universe Total Risk = Unsystematic Risk + Systematic Risk Standard Deviation = Beta (from CAPM) + Variance of the Disturbance (Actual – Expected) Why do more assets = less risk? More assets = more likely that the movement of the assets cancel each other out Total risk of the portfolio decreases, but at a decreasing rate when # of assets increases State Prob R of Stock R of Bond Recession 0.30 -0.11 0.16 Normal 0.40 0.13 0.06 Boom 0.30 0.27 -0.04 If you invest $60 in stocks and $40 in bonds what are your portfolio weights? Stock = 60% and Bond = 40% Method 1 1. Find Er of each asset – Er = P1R1 + P2R2 Er of stocks = .3(-0.11) + .4(0.13) + .3(0.27) = .1 Er of bonds = .3(0.16) + .4(0.06) + .3(-.04) = 0.06 2. Find Er of each portfolio by applying the probabilities – Er = Wa * Era + Wb * Erb Er of portfolio = .6*.1 + .4*.06 = 8.4% Method 2 1. Find Er for each outcome E recession = .6*-.11 + .4*0.16 = -.002 E normal = .6*.13 + .4*0.06 = .102 E boom = .6*.27 + .4*-.04 = .146 2. Find Er for each portfolio by applying the probabilities .3*-.002 + .4*.102 + .3*.146 = 8.4% 2 Asset Portfolio Variance and SD w a Stock and Bond Variance = Wa2σa2 + Wb σ + 2[Wa x Wb x σa x σb x ρa,b] Total risk, interactive risk Ρ = covariance / σaσb σa x σb x ρab = covariance between a and b total risk = w x σ variance measures total risk – examines how returns of asset deviate from average return variance = Ps [Rs – E(Ra)] 2 covariance = Ps [Rs – E(Ra)] [Rs – E(Rb)] Correlation = covariance / st dev of a x st dev of b Portfolio risk with more than 2 assets – have to add on interactive risk between A, B, and C 2[Wa x Wb x σa x σb x ρa,b] 2[Wa x Wc x σa x σc x ρa,c] 2[Wc x Wb x σc x σb x ρc,b] Number of covariance terms = n(n-1) / 2 Example 1 Ws = 70%; Wb = 30%; St dev S = 14.92%; St dev B = 7.75% Covariance = st dev2 2x st dev b x correlation s, b = -1.14% Varianc
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